Characterization of the symmetric group by its non-commuting graph

‎The non-commuting graph \nabla(G) of a non-abelian group G is defined as‎ ‎follows‎: ‎its vertex set is G-Z(G) and two distinct vertices x and y are‎ ‎joined by an edge if and only if the commutator of x and y is not the‎ ‎identity‎. ‎In this paper we prove that if G is a finite group with‎ ‎\nabla(G) \cong \nabla(BS_n)‎, ‎then G \cong BS_n‎, ‎where BS_n‎ ‎is the symmetric group of degree n‎, ‎where n is a natural number‎.

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Keywords and phrases: non-commuting graph , symmetric group , Finite groups